We mention that the radiative
transitions of \(X(3872)\rightarrow \psi (2S) \gamma \)  and \(J/\psi \gamma \)  were studied in
Ref. [1]}, [2]}, where the \(X(3872)\)  was also treated as the \(\chi _{c1}(2P)\)  state.
It also shows that the radiative decay properties are consistent with the observations from the BaBar [3]} and
LHCb [4]}. This feature was regarded as evidence for \(X(3872)\)  being the \(\chi _{c1}(2P)\)  state. However, as studied by Refs. [5]}, [6]} the radiative decays of \(X(3872)\)  are shown to be driven by the short-ranged component of the wave function. Therefore, our results actually can be regarded as a support of such a view that the short-ranged wave function is from the \(\chi _{c1}(2P)\)  state instead of concluding that it is a \(\chi _{c1}(2P)\)  state. Since the physical state of \(X(3872)\)  is apparently different from a conventional charmonium state, and there have been tremendous works discussing its dynamics, we do not want to over-interpret it based on our approach.
